My spouse has hired a private investigator to tail me. Can I sue?

No, you cannot. There is no “law of privacy” in Singapore. The most you can do is get an injunction (a court order preventing a person from doing something). But to get this done, you’ll need to show that the PI is causing harm to you, your lifestyle and/or your profession, or harassing you. If he is keeping a safe distance and not bothering you directly, there isn’t much you can do, as this is part of the services he provides.